MAYBE

Problem:
 app(nil(),xs) -> nil()
 app(cons(x,xs),ys) -> cons(x,app(xs,ys))
 rev(nil()) -> nil()
 rev(cons(x,xs)) -> append(xs,rev(cons(x,nil())))
 shuffle(nil()) -> nil()
 shuffle(cons(x,xs)) -> cons(x,shuffle(rev(xs)))

Proof:
 Complexity Transformation Processor:
  strict:
   app(nil(),xs) -> nil()
   app(cons(x,xs),ys) -> cons(x,app(xs,ys))
   rev(nil()) -> nil()
   rev(cons(x,xs)) -> append(xs,rev(cons(x,nil())))
   shuffle(nil()) -> nil()
   shuffle(cons(x,xs)) -> cons(x,shuffle(rev(xs)))
  weak:
   
  Matrix Interpretation Processor:
   dimension: 1
   max_matrix:
    1
    interpretation:
     [shuffle](x0) = x0,
     
     [append](x0, x1) = x0 + x1,
     
     [rev](x0) = x0,
     
     [cons](x0, x1) = x0 + x1,
     
     [app](x0, x1) = x0 + x1 + 1,
     
     [nil] = 0
    orientation:
     app(nil(),xs) = xs + 1 >= 0 = nil()
     
     app(cons(x,xs),ys) = x + xs + ys + 1 >= x + xs + ys + 1 = cons(x,app(xs,ys))
     
     rev(nil()) = 0 >= 0 = nil()
     
     rev(cons(x,xs)) = x + xs >= x + xs = append(xs,rev(cons(x,nil())))
     
     shuffle(nil()) = 0 >= 0 = nil()
     
     shuffle(cons(x,xs)) = x + xs >= x + xs = cons(x,shuffle(rev(xs)))
    problem:
     strict:
      app(cons(x,xs),ys) -> cons(x,app(xs,ys))
      rev(nil()) -> nil()
      rev(cons(x,xs)) -> append(xs,rev(cons(x,nil())))
      shuffle(nil()) -> nil()
      shuffle(cons(x,xs)) -> cons(x,shuffle(rev(xs)))
     weak:
      app(nil(),xs) -> nil()
    Matrix Interpretation Processor:
     dimension: 1
     max_matrix:
      1
      interpretation:
       [shuffle](x0) = x0 + 1,
       
       [append](x0, x1) = x0 + x1,
       
       [rev](x0) = x0,
       
       [cons](x0, x1) = x0 + x1,
       
       [app](x0, x1) = x0 + x1,
       
       [nil] = 0
      orientation:
       app(cons(x,xs),ys) = x + xs + ys >= x + xs + ys = cons(x,app(xs,ys))
       
       rev(nil()) = 0 >= 0 = nil()
       
       rev(cons(x,xs)) = x + xs >= x + xs = append(xs,rev(cons(x,nil())))
       
       shuffle(nil()) = 1 >= 0 = nil()
       
       shuffle(cons(x,xs)) = x + xs + 1 >= x + xs + 1 = cons(x,shuffle(rev(xs)))
       
       app(nil(),xs) = xs >= 0 = nil()
      problem:
       strict:
        app(cons(x,xs),ys) -> cons(x,app(xs,ys))
        rev(nil()) -> nil()
        rev(cons(x,xs)) -> append(xs,rev(cons(x,nil())))
        shuffle(cons(x,xs)) -> cons(x,shuffle(rev(xs)))
       weak:
        shuffle(nil()) -> nil()
        app(nil(),xs) -> nil()
      Matrix Interpretation Processor:
       dimension: 1
       max_matrix:
        1
        interpretation:
         [shuffle](x0) = x0 + 1,
         
         [append](x0, x1) = x0 + x1 + 1,
         
         [rev](x0) = x0 + 1,
         
         [cons](x0, x1) = x0 + x1,
         
         [app](x0, x1) = x0 + x1,
         
         [nil] = 1
        orientation:
         app(cons(x,xs),ys) = x + xs + ys >= x + xs + ys = cons(x,app(xs,ys))
         
         rev(nil()) = 2 >= 1 = nil()
         
         rev(cons(x,xs)) = x + xs + 1 >= x + xs + 3 = append(xs,rev(cons(x,nil())))
         
         shuffle(cons(x,xs)) = x + xs + 1 >= x + xs + 2 = cons(x,shuffle(rev(xs)))
         
         shuffle(nil()) = 2 >= 1 = nil()
         
         app(nil(),xs) = xs + 1 >= 1 = nil()
        problem:
         strict:
          app(cons(x,xs),ys) -> cons(x,app(xs,ys))
          rev(cons(x,xs)) -> append(xs,rev(cons(x,nil())))
          shuffle(cons(x,xs)) -> cons(x,shuffle(rev(xs)))
         weak:
          rev(nil()) -> nil()
          shuffle(nil()) -> nil()
          app(nil(),xs) -> nil()
        Bounds Processor:
         bound: 1
         enrichment: match
         automaton:
          final states: {7}
          transitions:
           cons1(7,19) -> 7*
           cons1(7,27) -> 28*
           app1(19,7) -> 19*
           append1(27,29) -> 29*
           append1(7,29) -> 18,7
           append1(19,29) -> 18,7
           rev1(7) -> 18*
           rev1(19) -> 18*
           rev1(28) -> 29*
           nil1() -> 19,18,27
           shuffle1(18) -> 19*
           app0(7,7) -> 7*
           cons0(7,7) -> 7*
           rev0(7) -> 7*
           append0(7,7) -> 7*
           nil0() -> 7*
           shuffle0(7) -> 7*
         problem:
          strict:
           app(cons(x,xs),ys) -> cons(x,app(xs,ys))
           rev(cons(x,xs)) -> append(xs,rev(cons(x,nil())))
          weak:
           shuffle(cons(x,xs)) -> cons(x,shuffle(rev(xs)))
           rev(nil()) -> nil()
           shuffle(nil()) -> nil()
           app(nil(),xs) -> nil()
         Matrix Interpretation Processor:
          dimension: 2
          max_matrix:
           [1 1]
           [0 1]
           interpretation:
                            [1 1]  
            [shuffle](x0) = [0 1]x0,
            
                               [1 0]     [1 0]  
            [append](x0, x1) = [0 0]x0 + [0 0]x1,
            
                        [1 1]  
            [rev](x0) = [0 0]x0,
            
                             [1 1]          [0]
            [cons](x0, x1) = [0 0]x0 + x1 + [1],
            
                            [1 1]     [1 1]  
            [app](x0, x1) = [0 1]x0 + [0 0]x1,
            
                    [0]
            [nil] = [0]
           orientation:
                                 [1 1]    [1 1]     [1 1]     [1]    [1 1]    [1 1]     [1 1]     [0]                     
            app(cons(x,xs),ys) = [0 0]x + [0 1]xs + [0 0]ys + [1] >= [0 0]x + [0 1]xs + [0 0]ys + [1] = cons(x,app(xs,ys))
            
                              [1 1]    [1 1]     [1]    [1 1]    [1 0]     [1]                                
            rev(cons(x,xs)) = [0 0]x + [0 0]xs + [0] >= [0 0]x + [0 0]xs + [0] = append(xs,rev(cons(x,nil())))
            
                                  [1 1]    [1 1]     [1]    [1 1]    [1 1]     [0]                           
            shuffle(cons(x,xs)) = [0 0]x + [0 1]xs + [1] >= [0 0]x + [0 0]xs + [1] = cons(x,shuffle(rev(xs)))
            
                         [0]    [0]        
            rev(nil()) = [0] >= [0] = nil()
            
                             [0]    [0]        
            shuffle(nil()) = [0] >= [0] = nil()
            
                            [1 1]      [0]        
            app(nil(),xs) = [0 0]xs >= [0] = nil()
           problem:
            strict:
             rev(cons(x,xs)) -> append(xs,rev(cons(x,nil())))
            weak:
             app(cons(x,xs),ys) -> cons(x,app(xs,ys))
             shuffle(cons(x,xs)) -> cons(x,shuffle(rev(xs)))
             rev(nil()) -> nil()
             shuffle(nil()) -> nil()
             app(nil(),xs) -> nil()
           Open